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Table Of Integrals Series And Products

This paper presents an analytical solver which is known as a generalization of types methodologies. With the proposed method, one of the old but at the same time popular problem is considered, which is known as nonlinear Zoomeron equation, and its analytical solutions are tried to obtain. Moreover, the known solutions, many new analytical solutions are obtained via the proposed method. Plotting some simulations of the solutions, we can present a conclusion.

Novel explicit solutions for the nonlinear Zoomeron equation by using newly extended direct algebraic technique

In this paper, we concern ourselves with the nonlinear Kadomtsev–Petviashvili equation (KP) with a competing dispersion effect. First we examine the integrability of governing equation via using the Painleve analysis. We next reduce the KP equation to a one-dimensional with the help of Lie symmetry analysis (LSA). The KP equation reduces to an ODE by employing the Lie symmetry analysis. We formally derive bright, dark and singular soliton solutions of the model. Moreover, we investigate the stability of the corresponding dynamical system via using phase plane theory. Graphical representation of the obtained solitons and phase portrait are illustrated by using Maple software.

A (2+1)-dimensional Kadomtsev-Petviashvili equation with competing dispersion effect: Painlevé analysis, dynamical behavior and invariant solutions

Lie symmetry analysis, optimal system, new solitary wave solutions and conservation laws of the Pavlov equation

In this paper, we study on the numerical solution of fractional nonlinear system of equations representing the one-dimensional Cauchy problem arising in thermoelasticity. The proposed technique is ...

Iterative method applied to the fractional nonlinear systems arising in thermoelasticity with mittag-leffler kernel

In this work, we analytically examine a (3+1)-dimensional generalized Korteweg-de Vries-Zakharov-Kuznetsov equation (gKdV-ZKe) Solutions of this equation, including a non-topological soliton, are obtained by Lie symmetry reductions and direct integration Moreover, Kudryashov’s method is utilized to generate some closed-form solutions of the equation Furthermore, cnoidal and snoidal periodic wave solutions are displayed for a special case of the gKdV-ZKe The obtained solutions are presented graphically Conclusively, we provide conservation laws of gKdV-ZKe by engaging Noether’s theorem

A study of (3+1)-dimensional generalized Korteweg-de Vries- Zakharov-Kuznetsov equation via Lie symmetry approach

In this paper we study the modified equal-width equation, which is used in handling simulation of a single dimensional wave
propagation in nonlinear media with dispersion processes. Lie point symmetries of this equation are computed and used
to construct an optimal system of one-dimensional subalgebras. Thereafter using an optimal system of one-dimensional
subalgebras, symmetry reductions and new group-invariant solutions are presented. The solutions obtained are cnoidal
and snoidal waves. Furthermore, conservation laws for the modified equal-width equation are derived by employing two
different methods; the multiplier method and Noether approach.

On optimal system, exact solutions and conservation laws of the modified equal-width equation

In this work, we examine a nonlinear partial differential equation of fluid mechanics, namely, the generalized nonlinear advection–diffusion equation, which portrays the motion of buoyancy driven plume in a bent-on porous medium. Firstly, we classify all (point) symmetries of the equation, which prompt three cases of n. Next, for each case, we construct an optimal system of one-dimensional subalgebras and use them to perform symmetry reductions and symmetry invariant solutions. In a bid to explain the physical significance of some invariant solutions secured, we present a graphic display of some solutions in 3D, 2D as well as density plots via the exploitation of numerical simulations. Besides, we categorically state here that the results obtained in this study are new when compared with the outcomes previously achieved by Loubens et al., 2011 Quart. Appl. Math. 69 389–401. Interestingly, kink shape soliton, dark soliton, singular soliton together with exponential function solution wave profiles are displayed to make this work more valuable. Furthermore, we determine the conserved vectors in two different ways: engaging the general multiplier approach and Ibragimov’s conservation law theorem. Finally, we provide the physical meaning of these conservation laws.

A study of the generalized nonlinear advection-diffusion equation arising in engineering sciences

In this article, we examine a (3+1)-dimensional generalized breaking soliton equation which is highly applicable in the fields of engineering and nonlinear sciences. Closed-form solutions in the form of Jacobi elliptic functions of the underlying equation are derived by the method of Lie symmetry reductions together with direct integration. Moreover, the (G′/G)-expansion technique is engaged, which consequently guarantees closed-form solutions of the equation structured in the form of trigonometric and hyperbolic functions. In addition, we secure a power series analytical solution of the underlying equation. Finally, we construct local conserved vectors of the aforementioned equation by employing two approaches: the general multiplier method and Ibragimov’s theorem.

https://www.mdpi.com/2227-7390/8/10/1692/pdf

Closed-Form Solutions and Conserved Vectors of a Generalized (3+1)-Dimensional Breaking Soliton Equation of Engineering and Nonlinear Science

Dynamics of soliton waves of group-invariant solutions through optimal system of an extended KP-like equation in higher dimensions of medical sciences and mathematical physics

Oke Davies Adeyemo

Papers

A study of (3+1)-dimensional generalized Korteweg-de Vries- Zakharov-Kuznetsov equation via Lie symmetry approach

On optimal system, exact solutions and conservation laws of the modified equal-width equation

A study of the generalized nonlinear advection-diffusion equation arising in engineering sciences

Closed-Form Solutions and Conserved Vectors of a Generalized (3+1)-Dimensional Breaking Soliton Equation of Engineering and Nonlinear Science

Dynamics of soliton waves of group-invariant solutions through optimal system of an extended KP-like equation in higher dimensions of medical sciences and mathematical physics